Theory determination of $$\varvec{\bar{B}\rightarrow D^{(*)}\ell ^-\bar{\nu }}$$ form factors at $$\varvec{\mathcal {O}(1/m_c^2)}$$

Abstract

AbstractWe carry out an analysis of the full set of ten $$\bar{B}\rightarrow D^{(*)}$$B¯→D(∗) form factors within the framework of the Heavy-Quark Expansion (HQE) to order $$\mathcal {O}\left( \alpha _s,\,1/m_b,\,1/m_c^2\right) $$Oαs,1/mb,1/mc2, both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD light-cone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions in $$\bar{B}\rightarrow D^{(*)}\lbrace e^-,\mu ^-\rbrace \bar{\nu }$$B¯→D(∗){e-,μ-}ν¯ measurements. The coefficients entering at the $$1/m_c^2$$1/mc2 level are found to be of $$\mathcal {O}(1)$$O(1), indicating convergence of the HQE. The phenomenological implications of our study include an updated exclusive determination of $$|V_{cb}|$$|Vcb| in the HQE, which is compatible with both the exclusive determination using the BGL parametrization and with the inclusive determination. We also revisit predictions for the lepton-flavour universality ratios $$R_{D^{(*)}}$$RD(∗), the $$\tau $$τ polarization observables $$P_\tau ^{D^{(*)}}$$PτD(∗), and the longitudinal polarization fraction $$F_L$$FL. Posterior samples for the HQE parameters are provided as ancillary files, allowing for their use in subsequent studies.